2001 - JAMB Mathematics Past Questions and Answers - page 4

y = x sin x
dy/dx = 1 x sinx + x cosx
= sinx + x cosx
At x = π/2, = sin (π/2) + (π/2) cos (π/2)
= 1 + (π/2) x (0) = 1

Let the rectangle be a square of sides p/4.

So that perimeter of square = 4p
4 x (p/4) = p.

Mode = score with highest frequency = 11.
Square of 11 = 121

Mode = score with highest frequency = 11.
Square of 11 = 121

Mean = ∑fx/∑f
Mean = (4x3) + (7x5) + ... + (8x1) all divided by 20
Mean = 174/20 = 8.7

P (games end in draw)
=> Team P wins and Q wins
P(P wins) = 1/2
P(Q wins) = 1/2
Therefore P (games ends in draw) = 1/2 x 1/2 = 1/4

6P^r = 6 Thus r = 1

N.B 6P¹ = \(\frac{\text{6!}}{\text{(6 - 1)!}}\)

= \(\frac{\text{6!}}{\text{5!}}\)

= \(\frac{6 \times \text{5!}}{\text{5!}}\) = 6

6P_{r + 1} = 6P₂ = \(\frac{\text{6!}}{(6 - 2)\text{!}} = \frac{6\text{!}}{\text{4!}}\)

= \(\frac{6 \times 5 \times \text{4!}}{\text{4!}}\)

= 30

Total number of beads = 15.
Number of white beads = 4. => P(white) = 4/15.
Number of blue beads = 1. => P(blue) = 1/15.

P(white or blue) = P(white) + P(blue) = 5/15 = 1/3

\(The \hspace{1mm}mean \hspace{1mm} \bar{x} = \frac{\sum{x}}{n}=\frac{30}{6}=5\Variance\hspace{1mm}=\frac{\sum({x-\bar{x}})^{2}}{n}=\frac{30}{6}=5\)

Combination is the (n) number of ways of selecting a number of (r) subjects from n.
nCr = n!/r!(n-r)! = 12! 8! x 4! = 495